Introduction

Magnetic fields are a major agent in the interstellar medium (ISM) of spiral,
barred, irregular and dwarf galaxies.
They contribute significantly to the total pressure which balances the ISM
against gravity. They may affect the gas flows in spiral arms, around bars and
in galaxy halos. Magnetic fields are essential for the onset of star
formation as they enable the removal of angular momentum from the
protostellar cloud during its collapse. MHD turbulence distributes
energy from supernova explosions within the ISM. Magnetic reconnection
is a possible heating source for the ISM and halo gas. Magnetic fields
also control the density and distribution of cosmic rays in the ISM.

Radio galaxies form a separate class and are not considered in this article.
They are powered by violent processes around
black holes in their centers and show jets and radio lobes in the radio range, hosting
strong magnetic fields and energetic cosmic-ray particles.

Galactic magnetic fields can be observed in the optical range via starlight which is
polarized by interstellar dust grains in the foreground. These grains are elongated
and can be aligned by magnetic fields, where the major axis becomes perpendicular to the field lines.
Measurements of many stars revealed a general picture of the magnetic field in the Milky Way near
the Sun. Aligned dust grains also emit polarized infrared emission, which is very useful
to show magnetic fields in dust clouds in the Milky Way. Zeeman splitting of
radio spectral lines allows measurement of relatively strong fields in nearby, dense
gas clouds in the Milky Way. For those three techniques observations in external galaxies are
still difficult to obtain. The fourth technique, measuring synchrotron emission, is
the most powerful one and can be applied over the whole Milky Way, to nearby galaxies, and
also to distant galaxies.

Cosmic-ray electrons in galaxies are believed to be accelerated in the shock fronts of supernova remnants.
They propagate into the interstellar medium
and spiral around interstellar magnetic field lines with almost the speed of light.
They emit synchrotron emission over a large range of radio wavelengths.
The intensity of synchrotron emission increases with observation wavelength to a power of about 0.8.
The most energetic electrons can even emit synchrotron infrared or optical light.

The intensity
of synchrotron emission is a measure of the density of cosmic-ray electrons and
of the strength of the total magnetic field component in the sky plane.
The degree of linear polarization of synchrotron emission can be as high as
75% in a completely ordered field, which is a field with a constant orientation
within the volume traced by the telescope's beam. Any variation of the field
orientation within the beam reduces the degree of polarization. Regular fields are
believed to be generated e.g. by a dynamo (see below). Polarized emission can also
emerge from anisotropic turbulent fields (with random orientations in two dimensions),
which are generated from isotropic turbulent fields (with random orientations in three dimensions) by
compressing or shearing gas flows and frequently reverse their field direction by
180 degrees on scales smaller than the telescope beam.
Unpolarized synchrotron emission indicates isotropic turbulent fields
that have been generated by turbulent gas flows.
Hence, three components of the total field are distinguished by observations:
regular, anisotropic turbulent and isotropic turbulent fields.

The degree of synchrotron polarization in galaxies is observed to be 10-20% on average, indicating that isotropic
turbulent fields dominate in galaxies. Locally, 50% is observed (e.g. in the interarm regions of NGC 6946, see Fig.2 below);
the regular and/or anisotropic turbulent field dominates in such regions.

The intrinsic orientation of the observed polarization plane of an electromagnetic wave is
perpendicular to the field orientation. When the wave travels through a magnetized plasma,
the orientation of the polarization plane is changed by Faraday rotation. The rotation angle
increases with the plasma density, the strength of the component of the regular field along
the line of sight, and the square of the observation wavelength. Fields directed
towards us cause an anticlockwise sense of rotation, fields directed away from
us a clockwise rotation. Anisotropic and isotropic turbulent fields do not Faraday-rotate.
For typical plasma densities and regular field strengths in the interstellar medium
of galaxies, Faraday rotation becomes significant at wavelengths larger than
a few centimeters. At decimeter wavelengths, Faraday rotation is generally strong and
can lead to Faraday depolarization. In the meterwave range (below frequencies of
about 300 MHz), polarized emission from galaxies is generally too weak to be detected.

Measurement of the Faraday rotation from multi-wavelength observations allows us to determine
the strength and direction of the regular field component along the line of sight.
Combination with the polarization vectors yields a fully three-dimensional
picture of the magnetic field.

A second method to measure magnetic fields in galaxies is offered by bright and compact
polarized background sources (e.g. quasars or radio galaxies). Their polarized emission
can be Faraday-rotated within the interstellar medium of the foreground galaxy, proportional
to the strength of the interstellar magnetic field. This method suffers less from
Faraday depolarization and hence can be applied also to frequencies below 300 MHz.

The most sensitive instruments for radio polarization measurements are the
single-dish telescopes in Effelsberg (Germany, 100 m diameter) and in Parkes (Australia,
64 m diameter), and the synthesis (interferometer) telescopes in Westerbork (Netherlands),
the Jansky Very Large Array (USA), and the Australia Telescope Compact Array.
Low-frequency instruments like LOFAR did not yet detect polarization from galaxies
because of strong Faraday depolarization at long wavelengths.
A major increase in sensitivity and angular resolution is expected from the
Square Kilometre Array and its precursor telescopes (see below).

The Origin of Galactic Magnetic Fields

The origin of the first magnetic fields in the Universe is still a mystery (Widrow 2002).
Protogalaxies probably were already magnetic due to field ejection from the first
stars or from jets generated by the first black holes. However, a primordial
field in a young galaxy is hard to maintain because a galaxy rotates differentially
(the angular velocity decreases with radius), so that the magnetic
field lines get strongly wound up (in contrast to observations, see below) and
field lines with opposite polarity may cancel via magnetic reconnection.
This calls for a mechanism to sustain and organize the magnetic field.

The most promising mechanism is the dynamo which transfers mechanical energy
into magnetic energy (e.g. Beck et al. 1996,
Brandenburg & Subramanian 2005). With a suitable configuration of the fluid or gas
flow, a strong magnetic field with a stationary or oscillating configuration can be
generated from a weak seed field. Seed fields could have been generated in the early
Universe, e.g. at phase transitions, or in shocks in protogalactic halos (Biermann battery),
or in fluctuations in the protogalactic plasma.

In astronomical objects like stars,
planets or galaxies, an efficient dynamo needs turbulent motions and non-uniform
(differential) rotation and is called alpha-Omega dynamo. It generates
large-scale regular fields, even if the seed field was turbulent (order out of chaos).
The regular field structure obtained in dynamo models is described by modes of
different azimuthal symmetry in the disk and vertical symmetry perpendicular to the disk
plane. Such modes can be identified from the pattern of polarization angles and Faraday
rotation in multi-wavelength radio observations. Several modes can be excited in the
same object.

In spherical bodies like stars
or planets or galactic halos, the strongest mode is a double torus near the equator
with a reversal across the equatorial plane, surrounded by a dipolar field
(odd vertical symmetry). In flat objects like galactic disks, the strongest mode
is a single torus in the plane with a field of axisymmetric spiral shape,
without reversals, surrounded by a weaker quadrupolar field (even vertical symmetry).
This mode is frequently observed.
The next mode, of bisymmetric spiral shape with two field reversals in
the disk, possibly excited by gravitational interaction, seems to be rare.
The next higher quadrisymmetric mode can be excited by spiral arms and was found in many spiral galaxies,
though weaker than the axisymmetric mode. A large-scale field reversal, like the one found in the Milky Way,
indicates a distortion of dynamo action, for example by gravitational interaction with a companion galaxy,
or could be a relic from early times when the magnetic field was still chaotic.

Results from Radio Observations

Magnetic Field Strengths in Galaxies

Total magnetic field strengths can be determined from the intensity of
total synchrotron emission, assuming energy balance (equipartition) between
magnetic fields and cosmic rays. This assumption seems valid on large spatial and
time scales, but deviations occur on local scales in galaxies.
The typical average equipartition strength for spiral galaxies is
about 10 μG (microGauss) or 1 nT (nanoTesla). For comparison, the Earth's magnetic
field has an average strength of about 0.3 G (30 μT).
Radio-faint galaxies like M 31 (Fig.3) and M 33, our Milky Way's neighbors, have weaker fields
(about 5 μG), while gas-rich galaxies with high star-formation rates,
like M 51 (Fig.1), M 83 and NGC 6946 (Fig.2), have 15 μG on average. In prominent spiral arms
the field strength can be up to 25 μG, in regions where also cold gas and dust are concentrated.
The strongest total equipartition fields (50-100 μG) were found in starburst galaxies,
for example in M 82 and the Antennae, and in nuclear starburst regions, for example in the centers
of NGC 1097 and of other barred galaxies.

Galactic fields are sufficiently strong to be dynamically important: they drive mass inflow
into the centers of galaxies, they modify the formation of spiral arms and they can affect
the rotation of gas in the outer regions of galaxies. Magnetic fields provide the transport
of angular momentum required for the collapse of gas clouds and hence the formation of new stars.

The degree of radio polarization within the spiral arms is only a few %; the field in
the spiral arms must be mostly tangled. The ordered (regular or anisotropic) fields
traced by polarized synchrotron emission are generally strongest (10-15 μG) in the regions
between the optical spiral arms. This can possibly be explained by a dynamo wave which is phase
shifted with respect to the density wave producing the spiral arms.

Figure 1: Optical image of the spiral galaxy M 51 obtained with the Hubble Space Telescope (from Hubble Heritage), overlaid by contours of the total radio intensity and polarization vectors at 6cm wavelength, combined from radio observations with the Effelsberg and VLA radio telescopes (from Fletcher et al. 2011). The magnetic field follows well the optical spiral structure, but the regions between the spiral arms also contain strong and ordered fields. The bar in the top right corner indicates a scale of 1 arcminute or about 9000 light years (about 3 kiloparsecs) at the distance of the galaxy. Copyright: MPIfR Bonn

Magnetic Field Structures in Spiral Galaxies

The magnetic field forms nice spiral patterns in almost every galaxy, even in flocculent and
bright irregular types which lack any spiral optical structure (Beck & Wielebinski 2013).
This is regarded as a strong argument for the action of galactic dynamos.
Spiral fields are also observed in the central regions of galaxies and in circum-nuclear
rings of gas. In galaxies with
massive spiral arms, the magnetic field lines run mostly parallel to the optical arms,
but are concentrated at the inner edge of the spiral arms or between the spiral arms
(as an example, see Fig.1).
In several galaxies, the field forms independent magnetic arms between the arms,
as in NGC 6946 (Fig.2).
In galaxies with massive bars, the field pattern seems to follow the gas flow.
As the gas rotates faster than the spiral or bar pattern of a galaxy, a shock occurs
in the cold gas which has a small sound speed, while the warm, diffuse gas is only
slightly compressed. As the observed compression of the field in spiral arms and bars
is also small, the ordered field is coupled to the warm gas and is strong enough
to affect the flow of the warm gas.

Figure 2: Optical image of the spiral galaxy NGC 6946 in the Hα line (from Ferguson et al. 1998), overlaid by contours of the polarized radio intensity and radio polarization vectors at 6cm wavelength, combined from observations with the Effelsberg and VLA radio telescopes (from Beck and Hoernes 1996). This galaxy shows strong regular fields between the optical spiral arms. Copyright: MPIfR Bonn

Observations of the spiral galaxy IC 342, some 10 million light-years from Earth in the northern constellation Camelopardalis (the Giraffe),
with the Effelsberg and VLA radio telescopes revealed a surprising result (Beck 2015). A huge, helically-twisted loop coiled around the
galaxy's main spiral arm. Such a feature, never before seen in a galaxy, is strong enough to affect the flow of gas around the spiral arm.

Large-scale patterns of Faraday rotation observed in a few spiral galaxies reveal
regular fields with a large-scale constant direction, as predicted by dynamo models.
The Andromeda galaxy M 31 (Fig.3) hosts a dominating axisymmetric field,
the basic dynamo mode, which extends to at least 15 kpc distance from the centre
(one kiloparsec (kpc) corresponds to 3260 light years). Other candidates for a dominating
axisymmetric field are the nearby spiral IC 342 and the irregular Large Magellanic
Cloud (LMC). The field structures in M 51 and NGC 6946 (Figs.1 and 2) can be described by a
superposition of two dynamo modes. However, in most galaxies observed so far no
clear patterns of Faraday rotation could be found. Either many dynamo modes are
superimposed and cannot be distinguished with the limited sensitivity and resolution of
present-day telescopes, or most of the ordered fields traced by the polarization vectors
are anisotropic (with frequent reversals), due to shearing or
compressing gas flows.

Figure 3: Intensity of the total radio emission at 6cm wavelength (colours) and polarization vectors of the highly inclined Andromeda Galaxy, M 31, observed with the Effelsberg telescope (from Berkhuijsen, Beck and Hoernes 2003). The radio emission is concentrated in a ring-like structure at about 10 kiloparsec radius where the magnetic field is exceptionally regular on scales of several kiloparsecs. Copyright: MPIfR Bonn

Galaxies seen in edge-on view possess radio halos with exponential
scale heights of 1-2 kpc. The magnetic field orientations are mainly parallel
to the disk near the plane, but vertical components are visible at above and below
the plane and also at large distances from the center (Fig.4).
A prominent exception is the edge-on spiral galaxy NGC 4631 with the brightest and
largest radio halo observed so far, composed of vertical magnetic spurs connected to
star-forming regions in the disk. The observations support the idea of a
galactic wind which is driven by star formation in the disk and transports gas,
magnetic fields and cosmic-ray particles into the halo.

An extended review of magnetic fields in spiral galaxies can be found in Beck (2016).

Figure 4: Optical image in the Hα line of the spiral galaxy NGC 5775 which is seen almost edge-on, overlaid by contours of the intensity of the total radio emission at 6cm wavelength and polarization vectors, observed with the VLA (from Tüllmann et al. 2000). The field lines are parallel to the disk near the plane, but turn vertically above and below the disk. Copyright: Cracow Observatory

Magnetic Fields in the Milky Way

According to radio synchrotron, optical polarization and Zeeman splitting data,
the average strength of the total magnetic field in the Milky Way is about 6 μG near the
Sun and increases to 20-40 μG in the Galactic center region. Radio filaments near the Galactic center and dense clouds of cold molecular gas host fields of up to several mG strength (Heiles & Crutcher, in Wielebinski & Beck 2005). Outside the central region, the large-scale field is mostly parallel to the plane of the Galactic disk. Faraday rotation measurements from the polarized radio emission of pulsars with known distances allow to investigate the structure of the Milky Way's magnetic field in three dimensions with much higher resolution than in external galaxies. The overall field structure follows the optical spiral arms, like in other galaxies, but additionally one large-scale field reversal in the disk, inside the solar radius, and several distortions near star-forming regions were discovered (Beck & Wielebinski 2013). More large-scale field reversals in the disk have been proposed, but need confirmation by improved observations.

The diffuse polarized radio emission from the Milky Way as observed with radio telescopes and with the WMAP satellite and the Faraday rotation measures (RM) from polarized background sources were analyzed to obtain an overall model of the Milky Way's magnetic field (Sun et al. 2008, Jansson & Farrar 2012). The field reversal inside the solar radius was confirmed. The sign of the magnetic field in the disk is the same above and below the plane, but a field reversal in the Milky Way halo beyond about 1 kpc (about 3000 light years) height is required. Such a vertical reversal would be very hard to detect in external galaxies. New RM measurements of sources behind the Galactic plane by Van Eck et al. (2011) gave further evidence that the Milky Way hosts a spiral field with one reversal.

Radio polarization surveys of the Milky Way also revealed a wealth of parsec-scale structures in the magnetized interstellar medium (Reich 2006).

New and future Radio Telescopes

Present-day radio polarization observations are limited by sensitivity and angular
resolution. The best available spatial resolution is 100-300 pc (one parsec (pc)
corresponds to 3.26 light years) in the nearest spiral galaxies and 10 pc in the nearest galaxy, the Large Magellanic Cloud. The Jansky Very Large Array (VLA, https://public.nrao.edu/telescopes/vla) and the Square Kilometre Array (SKA, http://www.skatelescope.org), construction of phase 1 planned for 2020-2025 at two sites (Southern Africa and Western Australia), will have much improved sensitivity at centimetre and decimetre wavelengths (Carilli & Rawlings 2004, Beck 2010). The SKA will allow to study magnetic field structures in galaxies at resolutions more than 10 times better than today (Beck et al. 2015). The SKA will discover thousands of new pulsars in the Milky Way which will enormously increase the number of Faraday rotation measurements and hence provide a detailed map of the magnetic field structure.

At long wavelengths of a few metres, a new-generation radio telescope, the Low Frequency
Array (LOFAR), has started full operation in 2012. 38 of the 50 stations are operating in the Netherlands (http://www.lofar.org), six in Germany (http://www.lofar.de), three in Poland (http://www.oa.uj.edu.pl/lofar), and one each in the UK (http://www.lofar-uk.org), in
France (http://www.obs-nancay.fr/index.php/en/instruments/lofar), and in Sweden (http://lofar-se.org). Extension to further European countries are planned. Among many other observing possibilities, LOFAR is able to trace radio synchrotron emission from low-energy cosmic rays in weak magnetic fields. This allows us to observe the outermost regions of galaxies which are only accessible via radio waves. The first galaxy observed in detail is M 51 (Mulcahy et al. 2014).